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1.
采用线弹簧模型求解含焊接残余应力平板多个共面任意分布表面裂纹的应力强度因子.利用边裂纹权函数给出了裂纹表面上沿厚度非线性分布的残余应力向线性分布的转化公式.基于Reissner板理论和连续分布位错思想,将含多个共面任意分布表面裂纹的无限平板问题归结为一组Cauchy型奇异积分方程,并采用Gauss-Chebyshev方法获得了奇异积分方程的数值解.以三共面表面裂纹为例,计算了表面裂纹的应力强度因子,并讨论了裂纹间距、裂纹几何形状等因素对应力强度因子的影响.  相似文献   

2.
对无限大三维均质弹性体中任意平片裂纹的超奇异积分方程,巧妙地引入椭球坐标系和利用裂纹表面位移间断人有平方根的特性,获得了受任意方向均布压力作用下椭圆平片裂纹问题的超奇异积分方程的解析解。运用这些解析解和应力强度因子的定义,得到了裂纹前沿Ⅰ型、Ⅱ型和Ⅲ型和应力强度因子的精确表达式,所得结果与现有精确解完全一致。  相似文献   

3.
利用双材料位移基本解和Somigliana公式,将三维体内含垂直于双材料界面混合型裂纹问题归结为求解一组超奇异积分方程。使用主部分析法,通过对裂纹前沿应力奇性的分析,得到用裂纹面位移间断表示的应力强度因子的计算公式,进而利用超奇异积分方程未知解的理论分析结果和有限部积分理论,给出了超奇异积分方程的数值求解方法。最后,对典型算例的应力强度因子做了计算,并讨论了应力强度因子数值结果的收敛性及其随各参数变化的规律。  相似文献   

4.
本文由Reissner型板的不连续位移基本解,根据Betti互换定理,导出了Reissner型板的不连续位移边界积分方程,结合平面问题的不连续位移边界积分方程--边界元方法和线弹簧模型,给出了Reissner型板表面裂纹应力强度因子的线弹簧-不连续位移边界积分方程解法。  相似文献   

5.
本文利用三维断裂力学的超奇异积分方程求解理论,对三维无限体中两平行平片裂纹在任意载荷作用下的相互干扰问题作了研究。首先导出了以裂纹面移间断(位借)为未知函数的超奇异积分方程组,然后为其建立了有限积分边界元法;在此基础上,讨论用了裂纹面位移间断计算应力强度因子的方法,最后用此计算了两平行平片裂纹的相对位置对裂前沿应力强度因子的影响,其数值结果令人满意。  相似文献   

6.
横观各向同性材料的三维断裂力学问题   总被引:4,自引:0,他引:4  
陈梦成  张安哥 《力学学报》2006,38(5):612-617
从三维横观各向同性材料弹性力学理论出发, 使用Hadamard有限部积分概念, 导出了三维状态下单位位移间断(位错)集度的基 本解. 在此基础上, 进一步运用极限理论, 将任意载荷作用下, 三维无限大横观各向 同性材料弹性体中, 含有一个位于弹性对称面内的任意形状的片状裂纹问题, 归结为求 解一组超奇异积分方程的问题. 通过二维超奇异积分的主部分析方法, 精确地求得了裂纹前沿光滑点附近的应力奇异指数和奇异应力场, 从而找到了以裂纹表面位移间断表示的应力强度因子表达式及裂纹局部扩展所提供 的能量释放率. 作为以上理论的实际应用,最后给出了一个圆形片状裂纹问题 的精确解例和一个正方形片状裂纹问题的数值解例. 对受轴对称法向均布载荷作用下圆形片状裂纹问题, 讨论了超奇异积分方程的精确求解方法, 并获得了位移间断和应力强度因子的封闭解, 此结果与现有理论解完全一致.  相似文献   

7.
用超奇异积分方程法将多场耦合载荷作用下磁电热弹耦合材料内含任意形状 和位置三维多裂纹问题转化为求解一以广义位移间断为未知函数的超奇异积分方程组问题, 退化得到内含任意形状平行三维多裂纹问题的超奇异积分方程组;推导出平行三维多裂纹问 题的裂纹前沿广义奇异应力场解析表达式、定义了广义(应力、应变能)强度因子和广义能量 释放率;应用有限部积分概念及体积力法,为超奇异积分方程组建立了数值求解方法,编制 了FORTRAN程序,以平行双裂纹为例,通过典型算例,研究了广义(应力、应变能)强度因子 随裂纹位置、裂纹形状及材料参数变化规律,得到裂纹断裂评定准则. 最后,分析了裂纹间 干扰、屏蔽作用及其在工程实际中的应用.  相似文献   

8.
各向异性平面含斜裂纹的奇异积分方程方法   总被引:1,自引:0,他引:1  
张建勇  李星 《力学季刊》2004,25(2):248-255
本文应用平面弹性复变方法,将无限各向异性平面中的任意斜裂纹问题归结为求解一组解析函数边值问题,通过构造适当的积分变换将边值问题转化为奇异积分方程,进而应用Lobotto-Chebyshev数值求积公式,求出该奇异积分方程的数值解,并得到了应力强度因子的近似表达式,最后,给出了一些实例的数值结果,对特例的数值结果与精确结果进行比较,吻合的很好。  相似文献   

9.
曲线裂纹和反平面圆形夹杂相交问题   总被引:3,自引:0,他引:3  
建立了和反平面圆夹杂界面相交的曲线裂纹的弱奇异积分方程,利用Cauchy型奇异积分方程主部分析方法研究了穿过反平面圆夹杂界面的曲线裂纹在交点处的奇性应力指数以及交点处角形域内的奇性应力,并根据奇性应力定义了交点处的应力强度因子。通过对弱奇异积分方程的数值求解,可得裂纹端点和交点处的应力强度因子。  相似文献   

10.
给出了一组只包含Cauchy主值积分、不含有强奇异积分的三维静动力边界积分方程及其应用于裂纹问题的具体列式,并给出了几何轴对称问题的相应半解析边界元求解方法,将三维问题降阶为一维数值问题.文中分析了无限、半无限介质中圆裂纹、平行圆裂纹系、球面裂纹等在静载及应力波作用下的静力或瞬态动力响应问题,求得了相应的应力强度因子.  相似文献   

11.
In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.  相似文献   

12.
Investigated is a crack problem for an array of collinear microcracks in composite matrix. Inclusions are situated in between the neighbouring microcracks tips and exhibit different elastic properties than matrix. The problem is solved using the technique of distributed dislocations. A developed approximate fundamental solution for a single dislocation lying in a general point between inclusions is employed in the distribution of continuously distributed dislocation to cracks modelling. Stress intensity factor is calculated for various cracks/inclusions geometries and elastic moduli mismatches. Stability and/or instability of the straight microcrack paths is investigated for slowly growing microcracks with inclusions located in between the neighbouring microcracks tips. Applications to periodic microcrack tunnelling and microcracks weakening ahead of the main crack are discussed.  相似文献   

13.
In this paper, the interactions between an elliptic hole and an arbitrary distributed small crack in plane piezoelectric medium, which are often happened in engineering problems, are discussed. The Green’s functions in a piezoelectric plate with an elliptic hole for a generalized line dislocation and a generalized line force are presented. The small crack is represented by unknown continuous distributed dislocations. By considering traction free conditions on the surface of the small crack, the problem is then reduced to a group of singular integral equations which are solved by using a special numerical technique. Accuracy of the present method is confirmed by comparing the numerical results with those in literatures for PZT-4 when the elliptic hole is degenerated into a crack. The generalized stress intensity factors of cracks and the generalized stress on the edge of the elliptic hole are shown graphically. It is shown that the small crack may have shielding or amplifying effects on the main elliptic hole or crack, which depends on the location and orientation of the small crack. The hole near a crack can significantly reduce the stress intensity factor of the crack. The direction of the electric field is important to shielding effect.  相似文献   

14.
导电薄板内电流密度分布与反平面剪切的比拟   总被引:1,自引:0,他引:1  
定量分析电流密度在含裂纹载流薄板内的分布是当前利用电流热效应止裂技术中一个首先要解决的问题.由于裂纹的存在,电流密度在裂尖形成带奇异性分布的高度密集.现有的分析方法往往比较复杂或局限于特殊布置形式的裂纹.通过电流密度分布与弹性力学里反平面剪切问题的比拟,把分析含裂纹载流薄板内电流密度的分布等效于考虑相应的III型裂纹问题,并比照III型裂纹的应力强度因子来定义电流密度因子.而对于裂纹问题的处理可采用分布位错法这一断裂力学里便利有效的分析手段.由给出的算例可见,所提出的比拟解法可以方便精确地求解电流密度在裂尖附近的奇异分布,并有助于对这一奇异性在概念上的直观理解.  相似文献   

15.
The dynamic response of multiple coplanar interface cracks between two dissimilar piezoelectric strips subjected to mechanical and electrical impacts is investigated. Solutions to two kinds of electric boundary conditions on crack surfaces, i.e. electric impermeable and electric permeable, are obtained. Laplace and Fourier transforms and dislocation density functions are employed to reduce the mixed boundary value problem to Cauchy singular integral equations,which can be solved numerically. The effects of electrical load, geometry criterion of piezoelectric strips, relative location of cracks and material properties on the dynamic energy release rate are examined.  相似文献   

16.
The stress field, crack-tip plastic zones and total plastic displacement created around an infinite row of collinear elastoplastic constant width Griffith-type strip cracks moving within an orthotropic crystal are considered using the powerful method of dislocation layers. The method is applied with the BCS modelled elastoplastic cracks moving under mode III loading at constant crack-tip velocity, according to the Yoffe model. Simultaneously the analysis provides solutions for a corresponding single crack moving similarly within a finite orthotropic plate and a finite plate containing a surface crack. Analogous results for the corresponding mode I, mode II and purely elastic cracks can be deduced.  相似文献   

17.
The fracture behavior of a cracked strip under antiplane mechanical and inplane electrical loading is studied. A functionally graded piezoelectric strip with exponential material gradation is under consideration. The mechanical and electrical loading is combined via loading coupling factor. The problem of a graded piezoelectric strip containing a screw dislocation is solved. This solution results in stress and electric displacement components with Cauchy singularity. Based on the solution achieved for the dislocation, the distributed dislocation technique (DDT) is utilized to form any geometry of multiple cracks and analyze the behavior of a cracked strip under antiplane mechanical and inplane electrical loading. This technique is capable of the analysis of a strip with a system of interacting cracks. Several examples including strips with single crack, two straight cracks and two curved cracks are presented.  相似文献   

18.
本文采用考虑裂纹面上具有任意分布载荷的线弹簧模型,在Kirchhoff板弯曲理论的假设下,将含半椭圆型表面裂纹的平板问题化为一组耦合的积分方程组进行求解,对均匀拉伸和纯弯曲两种载荷作用下的应力强度因子数值解,同经典线弹簧模型和有限元解进行了比较,并给出了经典线弹簧模型不能得到的、裂纹面上承受幂次不均匀应力分布时应力强度因子的数值解.  相似文献   

19.
含内埋裂纹的板条瞬态响应分析   总被引:1,自引:0,他引:1  
利用线弹簧模型求解了阶跃载荷作用下含内埋裂纹的无限长板条问题,对采用基于线弹簧模型的解析方法求解三维裂纹动态问题作了有益的探索。定性解释了动态线弹簧采用静态线弹簧本构关系的可行性,通过积分变换方法,导出了描述内埋裂纹板条动态问题的Cauchy型奇异积分方程。进行了数值计算,对模型应用的合理性作了理论解释,并对内埋裂纹板条瞬态响应的影响因素作了细致的分析。  相似文献   

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